Robust option pricing

Chaithanya Bandi*, Dimitris Bertsimas

*Corresponding author for this work

Research output: Contribution to journalArticle

25 Scopus citations

Abstract

In this paper, we combine robust optimization and the idea of ∈-arbitrage to propose a tractable approach to price a wide variety of options. Rather than assuming a probabilistic model for the stock price dynamics, we assume that the conclusions of probability theory, such as the central limit theorem, hold deterministically on the underlying returns. This gives rise to an uncertainty set that the underlying asset returns satisfy. We then formulate the option pricing problem as a robust optimization problem that identifies the portfolio which minimizes the worst case replication error for a given uncertainty set defined on the underlying asset returns. The most significant benefits of our approach are (a) computational tractability illustrated by our ability to price multi-asset, American and Asian options using linear optimization; and thus the computational complexity of our approach scales polynomially with the number of assets and with time to expiry and (b) modeling flexibility illustrated by our ability to model different kinds of options, various levels of risk aversion among investors, transaction costs, shorting constraints and replication via option portfolios.

Original languageEnglish (US)
Pages (from-to)842-853
Number of pages12
JournalEuropean Journal of Operational Research
Volume239
Issue number3
DOIs
StatePublished - Dec 16 2014

Keywords

  • American option
  • Option pricing
  • Robust optimization
  • Volatility smile

ASJC Scopus subject areas

  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management

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